"Render Animation" doesn't refresh bone constraint to rendering frame in 2.8
I was having a similar problem.  My issue was I had one bone with a Damped Track constraint pointed at a another bone which had it's own Damped Track constraint pointed right back at the first bone.  It should have still worked since the tracking constraint didn't affect the location of either bone's head, but...  it apparently confused Blender anyway.  Ultimately, in order to fix the problem I had to create 2 more bones with no constraints in the same locations of the original 2 bones.  I could then have the original 2 bones point at those un-constrained bones.  In other words, having a constrained bone relying on another constrained bone can cause problems.